Jean-Marie De Koninck and Aleksandar Ivi\'c

Abstract: Several results concerning the set $\S$ are proved. This set was constructed by A. Granville as follows: Let $1\in\Cal S$, and for $n\in\Bbb N$ and $n>1$ let $n\in\Cal S$ if $\sum_{d|n,dKeywords: sum of divisors, perfect numbers, Mersenne primes